Final answer:
The average rate of change of the function f(x) = x^2 - 7x + 6 over the interval 1 < x < 9 is calculated by evaluating the function at x=1 and x=9, finding the difference, and dividing by the length of the interval, resulting in an average rate of change of 6 units per unit interval.
Step-by-step explanation:
The average rate of change of a function on an interval is the change in the function's value over the interval divided by the change in the interval itself. To calculate the average rate of change of the function f(x) = x2 - 7x + 6 over the interval 1 < x < 9, you evaluate the function at the endpoints of the interval and then subtract the values of f at these points, dividing by the length of the interval.
Evaluating the function at the endpoints:
- f(1) = 12 - 7(1) + 6 = 0
- f(9) = 92 - 7(9) + 6 = 48
Calculating the average rate of change:
Average rate = [f(9) - f(1)] / (9 - 1) = [48 - 0] / (8) = 6
Therefore, the average rate of change of f(x) over the interval 1 < x < 9 is 6 units per unit interval.